As a general rule, if saliva is swallowed along with some blood and the quantity of blood is more than or equal to the quantity of saliva, the fast is invalidated . But if the quantity of blood is less than the quantity of saliva, the fast remains valid.
1) In the concerned situation, if the fasting individual wokeup and was certain of the fact that they had swallowed saliva mixed with blood and that the quantity of blood was equal to or more than the saliva, then, according to the ruling stated above, their fast is invalidated and the individual must perform qaza for that day's fast. If they are not certain of this, their fast remains valid.

2) If a fasting person's teeth start bleeding while they are awake, and they swallow saliva mixed with blood, the same ruling will apply. If the quantity of blood is equal to, or more than the quantity of saliva, their fast is invalidated and the individual must perform qaza for that day’s fast although, kaffarah does not become obligatory. And if the quantity of saliva is more than the quantity of blood, the fast remains valid.